Question

Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.

Answer 1

Step-by-step explanation:

Given;

We are given two ice cream cups in the shapes of a cone and a cylinder.

The dimensions are;

`\begin{gathered} Cone: \\ Radius=4in \\ \\ Height=6in \\ \\ Cylinder: \\ Radius=3in \\ \\ Height=2in \end{gathered}`

Required;

We are required to determine which of the two cups will hold the most ice cream.

Step-by-step solution;

Take note that the radius of the cylinder was derived as follows;

`\begin{gathered} radius=(diameter)/(2) \\ \\ radius=(6)/(2)=3 \end{gathered}`

The volume of the cone is given by the formula;

`\begin{gathered} Volume=(1)/(3)\pi r^2h \\ \\ Therefore: \\ Volume=(1)/(3)*3.14*4^2*6 \\ \\ Volume=(3.14*16*6)/(3) \\ \\ Volume=100.48 \end{gathered}`

Rounded to the nearest tenth, the volume that the cone can hold will be;

`Vol_(cone)=100.5in^3`

Also, the volume of the cylinder is given by the formula;

`\begin{gathered} Volume=\pi r^2h \\ \\ Volume=3.14*3^2*2 \\ \\ Volume=3.14*9*2 \\ \\ Volume=56.52 \end{gathered}`

Rounded to the nearest tenth, the volume will be;

`Vol_(cylinder)=56.5in^3`

ANSWER:

Therefore, the results show that the CONE will hold the most ice cream.